Sort by squares and find k-th smallest

Given a nondecreasing sorted array of integers nums, do the following:

1. Reorder the original elements by increasing square value (equivalently, by absolute value). For elements whose squares are equal, any order is acceptable. Target time complexity strictly better than O(N log N); aim for O(N) time. Example: nums = [-3, -2, 0, 1, 2, 5] -> [0, 1, -2, 2, -3, 5].
2. Follow-up: Given the same nums and an integer k (1-indexed), return the k-th element in the order induced by sorting by square value, without fully materializing that order. You must not explicitly sort by squares; target O(log N) time. Clearly state your algorithm, complexity, and any assumptions.